# 17 cards numbered 1, 2, 3, 4, .... ,17 are put in a box and mixed thoroughly.

Question:

17 cards numbered 1, 2, 3, 4, .... ,17 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears

(i) an odd number

(ii) a number divisible by 5.

Solution:

Total number of cards = 17

(i) Let  E1 be the event of choosing an odd number.

These numbers are 1, 3, 5, 7, 9, 11, 13, 15 and 17.

$\therefore P($ getting an odd number $)=P\left(E_{1}\right)=\frac{\text { Number of outcomes favourable to } E_{1}}{\text { Number of all possible outcomes }}$

$=\frac{9}{17}$

Thus, the probability that the card drawn bears an odd number is $\frac{9}{17}$.

(i) Let  E2 be the event of choosing a number divisible by 5.

These numbers are 5, 10 and 15.

$\therefore P($ getting a number divisible by 5$)=P\left(E_{2}\right)=\frac{\text { Number of outcomes favourable to } E_{2}}{\text { Number of all possible outcomes }}$

$=\frac{3}{17}$

Thus, the probability that the card drawn bears a number divisible by 5 is $\frac{3}{17}$.